Determine the location of each local extremum of the function
$f(x)= -x^3 + 12x^2 - 45x - 2$
Critical values I found are $x=3$, and $x=5$
Critical points I found are $(3, -56) (5, -52)$
How do I find the local minimum/maximum?
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$\begingroup$Well because theres only two local extremums, the local maximum must be at $(5, -52)$ and the local minimum is at $(3, -56)$, as the cubic function is unbounded at the ends of (-$\infty$, $\infty$).
$\endgroup$ 0 $\begingroup$The local minimum or local maximum are points on your f(x) graph where there's a valley. You can find local maximum and local minimum value by using your critical points and plugging them into the second derivative. If the number f''(x)<0, then (x,f(x)) is a local max and if f''(x)>0, then it's a local min.
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